Non-standard quantum so(2,2) and beyond

Details Non-standard quantum so(2,2) and beyond Non-standard quantum so(2,2) and beyond

1994-06-15

arxiv.org/abs/hep-th/9406098v2

J.Phys. A28 (1995) 941-956

Physics

High Energy Physics

High Energy Physics - Theory

19 pages, LaTeX; final version

Scientific paper

10.1088/0305-4470/28/4/018

A new "non-standard" quantization of the universal enveloping algebra of the split (natural) real form $so(2,2)$ of $D_2$ is presented. Some (classical) graded contractions of $so(2,2)$ associated to a $Z_2 \times Z_2$ grading are studied, and the automorphisms defining this grading are generalized to the quantum case, thus providing quantum contractions of this algebra. This produces a new family of "non-standard" quantum algebras. Some of these algebras can be realized as (2+1) kinematical algebras; we explicitly introduce a new deformation of Poincar\'e algebra, which is naturally linked to the null plane basis. Another realization of these quantum algebras as deformations of the conformal algebras for the two-dimensional Euclidean, Galilei and Minkowski spaces is given, and its new properties are emphasized.

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